In the white-noise paraxial regime the Green's function \(\hat{\cal G}\)  is of the form [1]}
\(\hat{\cal G} (\omega ,L,{{\itbf x}}, {{\itbf y}}\big ) = \frac{i c_o}{2\omega } e^{i \frac{\omega }{c_o} L} \hat{G}(\omega , L,{{\itbf x}},{{\itbf y}}) ,\) 
